Dynamic Macroeconomics I Introduction to Real …economia.unipv.it/.../slides_lectures_RBC_introduction.pdf · Dynamic Macroeconomics I Introduction to Real Business ... and bene–t

Dynamic Macroeconomics IIntroduction to Real Business Cycle Theory

Lorenza RossiUniversity of Pavia

Sant�Anna di Pisa - Spring 2014Part of these slides are based on my Course of Advanced Macroeconomics IIheld at UPF and bene�t of the work done by Jordi Gali in preparing his course

of Macroeconomia Avanzada II at UPF.

University of Pavia ()Sant�Anna di Pisa - Spring 2014 Part of these slides are based on my Course of Advanced Macroeconomics II held at UPF and bene�t of the work done by Jordi Gali in preparing his course of Macroeconomia Avanzada II at UPF. 1

/ 64

Outline

Business Cycle De�nition and Facts

Measuring Business Cycle

Introduction: Lucas�methodological proposal

The Real Business Cycle Theory1 Data: measuring the business cycle2 The Basic Real business cycle model3 The solution of DSGE models: the Blanchard-Khan method4 Matching moments: Simulations with dynare codes

Evaluation of the RBC approach: the debate over RBC theory


/ 64

Evidence - US


/ 64

Evidence - US


/ 64

Evidence - US


/ 64

Evidence - US


/ 64

Evidence - Euro Area


/ 64



/ 64



/ 64



/ 64

De�nition of Business Cycle

Burns and Mitchel De�nition (1946) - "Measuring Business Cycle"NBER�Business cycles are a type of �uctuation found in the aggregate economicactivity of nations that organize their work mainly in business enterprises:a cycle consists of expansions occurring at the same time in manyeconomic activities, followed by similarly general recessions, contractionsand revivals which merge into the expansion phase of the next cycle; thissequence of changes is recurrent but not periodic; in duration, businesscycles vary from more than one year to ten or twelve years; they are notdivisible into shorter cycles of similar character with amplitudesapproximating their own.�


/ 64


Economy-wide �uctuations in economic activity around its long-termgrowth trend.

Expansions and contractions

Economic variables show comovements

Important to take into account possible leads and lags in timing wrt.real GDP

The business cycle is recurrent, but not periodic: it doesn�t occur atregular, predictable intervals

The business cycle is persistent

Since BC is persistent is important to study what causes BC and thepossible policies (�scal or monetary) useful to stabilize the economy


/ 64


Two key features

1 The comovement among individual economic variables (GDP,industrial production, uneployment, hours...).

2 The division of business cycles into separate phases: Expansions andContractions


/ 64

Business Cycle: Expansions and Contractions


/ 64

Business Cycle Expansions and Contractions

After a trough, activity increases in an expansion or boom until itreaches a peak

Business cycle: the sequence from one peak to the next, or fromone trough to the nextPeaks and troughs are turning pointsNBER for US and CEPR for EU are responsible for dating turningpoints and business cycle.


/ 64

Business Cycle Expansions and Contractions

All business cycles are characterized by common features, as for examplethe cyclical behavior of economic variables in terms of direction and timingwith respect to aggregate economic activity Y .

Direction:

Procyclical: in the same direction of YCountercyclical: in the opposite direction of YAcyclical: with no clear pattern

Timing:

LeadingLaggingCoincident


/ 64

Recession Dating - NBER

A recession is a signi�cant decline in economic activity spread acrossthe economy, lasting more than a few months, normally visible in realgross domestic product (GDP), real income, employment, industrialproduction, and wholesale-retail salesA recession begins just after the economy reaches a peak and ends asthe economy reaches its trough. Between trough and peak: anexpansion. Expansion is the normal state; most recessions are briefand they have been rare in recent decades.Because a recession in�uences the economy broadly and is notcon�ned to one sector, the committee emphasizes economy-widemeasures of economic activity.The committee views real GDP as the single best measure ofaggregate economic activity.The committee therefore places considerable weight on the estimatesof real GDP issued by the Bureau of Economic Analysis of the U.S.Department of Commerce.University of Pavia ()

Sant�Anna di Pisa - Spring 2014 Part of these slides are based on my Course of Advanced Macroeconomics II held at UPF and bene�t of the work done by Jordi Gali in preparing his course of Macroeconomia Avanzada II at UPF. 17/ 64

Recession Dating - NBER

The traditional role of the committee is to maintain a monthlychronology, however, and the BEA�s real GDP estimates are onlyavailable quarterly. For this reason, the committee refers to a varietyof monthly indicators to choose the exact months of peaks andtroughs.

It places particular emphasis on two monthly measures of activityacross the entire economy: (1) personal income less transferpayments, in real terms and (2) employment. Also: (3) industrialproduction and (4) the volume of sales of the manufacturing andwholesale-retail sectors adjusted for price changes.

The committee also looks at monthly estimates of real GDP such asthose prepared by Macroeconomic Advisers (seehttp://www.macroadvisers.com). Nevertheless, there is no �xed ruleabout which other measures contribute information to the process.


/ 64

Business Cycle Cronology - US

Turning points are o¢ cially designated by the NBER


/ 64

Business Cycle Cronology - US


/ 64

Business Cycle Cronology - EU

Centre for Economic Policy Research (CEPR)

- www.cepr.org/data/da- quarterly cronology Euro Area- recession: signi�cant decline in the level of economic activities in th EuroArea. Two or three consecutive months in which GDP, employment etcdecrease in the EU area, and showing a similar pattern in most countries- Four cycles since 1970- Last cycle: "peak": 2008Q1, "trough": 2009Q2,- Actual recession: "peak" 2011Q3 ("trough"?)- EuroCoin Indicator (CEPR): monthly coincident indicator of the euroarea business cycle available in real time


/ 64

EuroCoin - Centre for Economic Policy Research (CEPR)

EuroCoin Indicator (CEPR): monthly coincident indicator of theeuro area business cycle available in real time.

The indicator provides an estimate of the monthly growth of euroarea GDP �after the removal of:

measurement errors;seasonal and other short-run �uctuations.idiosyncratic components. The indicator aims to capture only commoncomponents of EU area BC

The indicator is available very quickly, before the GDP numbers arereleased


/ 64


What data was used to produce EuroCOIN?

The database used to construct EuroCOIN is organized into elevenblocks: industrial production, producer prices, consumer prices,monetary aggregates, interest rates, �nancial variables, exchangerates, surveys by the European Commission, surveys by nationalinstitutes, external trade, labour markets

More information:http://dev3.cepr.org/data/eurocoin/indepth/#indicator_constructed

SLIDES on EuroCoin prepared by Cepr:http://dev3.cepr.org/data/eurocoin/


/ 64



/ 64



/ 64

Important Questions

Which are the main features, or stylized facts, of business cycle?

Are business cycle alike across time and countries

Which sources?

Which propagation mechanisms?

Which is the role played by macroeconomic policies: monetary and�scal policies? Are they stabilizing?

Is it important to stabilize the business cycle? Which are theimplication of the stabilization policies in terms of welfare?

Is there a macro-economic model able to reproduce the main featuresof the business cycle?


/ 64

Measuring Business Cycle

Given a time series y1, y2, y3, ..., yT () fytgEach series can be decomposed in two parts: trend and cycle

yt = zt + xt

zt : long-run trendxt : : cyclical componentThe cyclical component is stationary.

To get the cyclical component we need to transform data intomean-zero covariance stationary stochastic processes

E fxtg = µ (usually with µ = 0)

Ef(xt � µ)(xt�k � µ)g = γ (k) < +∞..... 8t, per k = 1, 2, 3...


/ 64


/ 64

Measuring Business Cycle: Traditional decomposition

Traditional Business Cycle Theory: output trend zt evolvessmoothly over time,

zt = α0 + α1t

orzt = α0 + α1t + α2t2 + α3t3 + ...+ αqtq

Estimation

minfa0,α1g

T

∑t=1[yt � (α0 + α1t)]

2

Cycles are viewed as deviation from trends, i.e.

bxt = yt � bztwhere bzt is the estimated value of zt .Limits: eliminating a deterministic trend is not su¢ cient tostationarize the series if the series has a unit root.University of Pavia ()

Sant�Anna di Pisa - Spring 2014 Part of these slides are based on my Course of Advanced Macroeconomics II held at UPF and bene�t of the work done by Jordi Gali in preparing his course of Macroeconomia Avanzada II at UPF. 29/ 64

Measuring Business Cycle: Linear Trend


/ 64

Measuring Business Cycle: RBC decomposition

Nelson and Plosser (JME 1982): many macroeconomic variableshave a unit root.

RBC Theory: cycles can be explained also assuming that zt evolvesaccording to a random walk, i.e.,

zt = b+ zt�1 + ut .

In this case much of the movements in yt are due to movements in ztand rather then to trend deviations yt � ztNotice that

∆ (zt ) = zt � zt�1 = b+ utis stationary: we say it is di¤erence stationary (DS).

Limits: to much weight is attached to high frequencies (quarter toquarter) that are not related to cycles


/ 64

Hodrick-Prescott and Band Pass Filter

Starting point: the trend zt must follow the observed data yt closely.=) The trend should not �uctuate widly from quarter toquarter.They infer the trend from the following minimisation problem:

minfztgTt=1

T

∑t=1(yt � zt )2 + λ

T�1∑t=2

[(zt+1 � zt )� (zt � zt�1)]2

The �rst part ensures that the trend component tracks the data fairlywell.

The constraint prevents the change in the trend being too volatile.

The larger λ the smoother the changes in the growth of the trendhave to be.


/ 64

Hodrick-Prescott and Band Pass Filter

minfztgTt=1

T

∑t=1(yt � zt )2 + λ

T�1∑t=2

[(zt+1 � zt )� (zt � zt�1)]2

The larger λ the smoother the changes in the growth of the trendhave to be.

λ ! ∞ ! zt = α0 + α1t

λ ! 0! zt = ytHP suggest a value of λ = 1600 for quarterly data.

Advantages: �exibility to capture changes in trendCritics: the choice of λ should vary from variable to variable.


/ 64

Hodrick-Prescott Filter


/ 64

Hodrick-Prescott Filter


/ 64

Band Pass Filter - Baxter and King (Restat 1999)

This �lter allows to choose the frequency range associated with thecyclical component.Conventional Range: between 6 and 32 quarters.


/ 64

Using Alternative Filters

Macroeconomic series re�ect di¤erent components - an underlyingtrend, the business cycle component, seasonality, as well as purelyrandom �uctuations.

One can use hundreds of di¤erent �ltering methods

Unfortunately we can never with complete certainty claim that one�lter is better than another.

Ideally, the cyclical component extracted from any dataset should notvary greatly between di¤erent �lters.

However, this is not the case.


/ 64

Comparing Alternative Filters


/ 64

Comparing Alternative Filters


/ 64

BC Statistics

fxtg: stationary and with zero mean:.

Volatility

! Standard Deviation: σ(xt ) �p(1/T )∑ x2t

Persistence

! autocorrelation: ρ(xt , xt�1) � cov (xt ,xt�1)σ2(xt )

on

cov(xt , xt�1) � (1/T )∑ xtxt�1

Cyclicality

! correlation with cyclical component of real GDP: ρ(xt , yt ) � cov (xt ,yt )σ(xt )σ(yt )

or cov(xt , yt ) � (1/T )∑ xtytthe variable can be: procyclical (+), countercyclical (�), o acyclical

(' 0)


/ 64

BC Statistics

Table 1: Statistical Properties of the U.S. Business CycleHP-Filtered (1600), 1948Q1-2013Q3

σ(bxt ) σ(bxt )σ(byt ) ρ(bxt ,bxt�1) ρ(bxt , byt )

GDP 1.69 1.0 0.85 1.00Consumption 1.26 0.7 0.81 0.79Investment 4.95 2.9 0.89 0.80Gov.Purchases 3.41 2.0 0.90 0.20Hours Worked 1.98 1.2 0.91 0.88Labor Prod. 1.10 0.6 0.72 0.39TFP 1.32 0.8 0.77 0.76Real Wage 0.92 0.5 0.71 0.20Real Int. Rate 1.22 0.7 0.78 0.07

(1)


/ 64

Comovements


/ 64

BC Statistics

Table 2: Statistical Properties of the Euro Area Business CycleHP-Filtered (1600), 1970Q1-2012Q4


GDP 1.17 1.0 0.88 1.00Consumption 0.82 0.7 0.89 0.77Investment 2.92 2.5 0.89 0.92Gov.Purchases 0.58 0.5 0.73 -0.16Employment 0.68 0.6 0.96 0.77Labor Productivity 0.77 0.7 0.79 0.83TFP 0.86 0.7 0.82 0.94Real Wage 0.53 0.5 0.74 0.27Real Int. Rate 0.91 0.8 0.77 0.57


/ 64

BC Statistics

Table 3: Statistical Properties of the U.S. Business CycleBP-Filtered (6,32), 1948Q1-2012Q3


GDP 1.65 1.0 0.92 1.00Consumption 1.20 0.7 0.92 0.82Investment 4.69 2.8 0.93 0.81Gov. Spend. 3.40 2.1 0.94 0.24Hours 1.92 1.2 0.93 0.89Labor Prod. 1.04 0.6 0.89 0.40TFP 1.25 0.8 0.90 0.76Real Wage 0.85 0.5 0.91 0.23Real Int. Rate 1.16 0.7 0.89 0.02


/ 64

BC Statistics

Table 4: Statistical Properties of the Euro Area Business CycleBP-Filtered (6,32), 1970Q1-2012Q4


GDP 1.16 1.0 0.88 1.00Consumption 0.82 0.7 0.84 0.77Investment 2.92 2.5 0.89 0.92Gov.Purchases 0.58 0.5 0.73 -0.16Employment 0.68 0.6 0.96 0.77Labor Prod. 0.77 0.7 0.79 0.83TFP 0.86 0.7 0.82 0.94Real Wage 0.53 0.5 0.74 0.27Real Int. Rate 0.91 0.8 0.77 0.57


/ 64

Stylized Facts

1 Consumption is procyclical and less volatile than output2 Durable goods consumption is more volatile than non-durable goodsconsumption

3 Investment are more volatile than output4 Hours and employment are almost as volatile as output5 Wages are slightly procyclical or acyclical6 Productivity: procyclical and less volatile than output


/ 64

Stylized Facts


/ 64

International Business Cycle?


/ 64



/ 64



/ 64



/ 64



/ 64

International Business Cycle: Euro Area versus US


/ 64

Business Cycle Changes over time

Ahmed et al. 2004


/ 64

Business Cycle Changes over tim

Table 5: Changes in the U.S. Business Cycle (HP-Filter)1948-1983 1984-2007 Ratio 1984-2013 Ratio

(1) (2) (2)/(1) (3) (3)/(1)

GDP 2.05 0.93 0.45 1.07 0.52Consumption 1.47 0.75 0.51 0.91 0.61Invest 5.68 3.68 0.64 4.46 0.78Gov.Purchases 4.57 1.08 0.23 1.13 0.24Hours 2.11 1.44 0.68 1.70 0.80Aver.Lab Prod. 1.25 0.79 0.63 0.83 0.66TFP 1.60 0.73 0.47 0.79 0.49Real Wage 0.74 1.03 1.30 1.13 1.52Real Int. Rate 1.48 0.89 0.60 0.86 0.58


/ 64


Table 6: Changes in the Euro Area Business Cycle (HP-Filter)1970-1993 1994-2007 Ratio 1994-2012 Ratio

(1) (2) (2)/(1) (3) (3)/(1)

GDP 1.14 1.00 0.87 1.21 1.06Consumption 0.94 0.73 0.77 0.64 0.68Investment 2.76 2.68 0.97 3.10 1.12Gov.Purchases 0.57 0.44 0.77 0.56 0.98Employment 0.69 0.65 0.94 0.64 0.92Ave.Lab. Prod. 0.76 0.53 0.69 0.79 1.03TFP 0.84 0.65 0.77 0.90 1.07Real Wage 0.62 0.42 0.67 0.34 0.54Real Int. Rate 1.09 0.60 0.55 1.06 0.97


/ 64


Possible explanations of the Great Moderation

a) sectoral composition: manifacturing versus servicesb) Role played by the Government:

- aggregate demand- automatic stabilizers- countercyclical policies

c) more �exible labor marketd) role of �nancial market and crisis (deposits insurance, the LLR)g) "Good Policies, Good Practices or Good Luck?"


/ 64

TRADITIONAL BUSINESS CYCLE THEORY: output trend Ytevolves smoothly over time, Yt = a+ bt. Cycles are viewed asdeviation from trends, i.e. Yt � Yt

RBC THEORY: cycles can be explained also assuming that Ytevolves according to a random walk, i.e., Yt = b+ Yt�1 + ut . In thiscase much of the movements in Yt are due to movements in Yt andrather then to trend deviations Yt � Yt


/ 64

The Lucas Research Program and MethodologicalProposal

Lucas (�76,�77,�80,�87). Two important references:1 Lucas, R.E., 1976, Econometric Policy Evaluation: A Critique,Carnegie-Rochester Conference Series on Public Policy, Vol. 1, pp.19-46.

2 Lucas, R.E., 1987, Models of Business Cycles, 1985 Yrjö JahnssonLectures, Basil Blackwell, Oxford.

The Lucas�critique: Macroeconomists should build so-calledstructural models, i.e. models that are based on microeconomicsfoundations, maximizing households and �rms, �exible prices/wages,market clearing, etc.

1 Microeconomic foundations2 General Equilibrium3 Rational Expectations4 No distinction between micro and macro: Economic theory


/ 64

The Lucas Research Program and MethodologicalProposal

CONCLUSIONS

Modern macroeconomics should employ dynamic general equilibriummodels (DSGE), that is, a macroeconomic model should be theresults of the solution of dynamic optimization problems underuncertainty by optimizing agents populating the model economy.

Build a "laboratory economy": much more di¢ cult task than oldKeynesian theorizing

Kydland & Prescott (1982) accepted the challenge posed by Lucas:they built the �rst Real Business Cycle (RBC) model.


/ 64

Basic RBC model

Outline of the RBC methodology:

a discrete-time stochastic model of the economy populated by maximizinghouseholds and �rms

MAIN SOURCE OF FLUCTUATIONS:

The erratic nature of technological progress


/ 64

MAIN RESULT AND FIRST INTUITION

There is only one �nal good in the economy which is producedaccording to a constant return to scale (CRS) production function

Yt = AtF (Kt�1,Nt )

where ln(At/A) = at is an exogenous process of technologicalprogress (or total factor productivity TFP), which evolves accordingto:

ln(At/A) = ρa ln(At/A) + εa,t , εa,t � WN�0, σ2a

�i .i .d .

A positive shock to the TFP shifts �rms�labor demand and the AScurve

Movements in employment and economic activity are seen as thee¢ cient responses of a perfectly competitive economy to aproductivity shock. =) Movements from a Walrasian equilibrium toanother one.


/ 64

POSITIVE TECHNOLOGY SHOCK


/ 64

MAIN RESULTS OF RBC THEORY

Money short-run and long run neutrality =) classical dichotomy

Fluctuations of all variable (output, consumption, employment,investment...) are the optimal responses to exogenous changes in theeconomic environment (technology shocks, government spendingshocks)

Shocks are not always desirable. But once they occur, �uctuations inoutput, employment, consumption and other variables are the optimalresponses to them!!

Stabilization Policies are not necessaty


/ 64

Documents

Dynamic Macroeconomics I Introduction to Real …economia.unipv.it/.../slides_lectures_RBC_introduction.pdf · Dynamic Macroeconomics I Introduction to Real Business ... and bene–t